A Lattice Point Problem and Additive Number Theory

@article{Alon1995ALP,
  title={A Lattice Point Problem and Additive Number Theory},
  author={Noga Alon and Moshe Dubiner},
  journal={Combinatorica},
  year={1995},
  volume={15},
  pages={301-309}
}
For every dimension d ≥ 1 there exists a constant c = c(d) such that for all n ≥ 1, every set of at least cn lattice points in the d-dimensional Euclidean space contains a subset of cardinality precisely n whose centroid is also a lattice point. The proof combines techniques from additive number theory with results about the expansion properties of Cayley graphs with given eigenvalues. 

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